Real hypersurfaces in complex two-plane Grassmannians with recurrent shape operator.

Kim, Seonhui; Lee, Hyunjin; Yang, Hae Young

Displaying similar documents to “Real hypersurfaces in complex two-plane Grassmannians with recurrent shape operator.”

On complete spacelike hypersurfaces with $R = a H + b$ in locally symmetric Lorentz spaces

Yingbo Han, Shuxiang Feng, Liju Yu (2011)

Archivum Mathematicum

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In this note, we investigate $n$ -dimensional spacelike hypersurfaces $M^{n}$ with $R = a H + b$ in locally symmetric Lorentz space. Two rigidity theorems are obtained for these spacelike hypersurfaces.

A remark on almost umbilical hypersurfaces

Julien Roth (2013)

Archivum Mathematicum

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In this article, we prove new stability results for almost-Einstein hypersurfaces of the Euclidean space, based on previous eigenvalue pinching results. Then, we deduce some comparable results for almost umbilical hypersurfaces.

On real hypersurfaces in quaternionic projective space with $𝒟^{⊥}$ -recurrent second fundamental tensor.

Suh, Young Jin, Pérez, Juan de Dios (1999)

International Journal of Mathematics and Mathematical Sciences

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Real hypersurfaces in complex space forms concerned with the local symmetry

Seon Mi Lyu, Juan de Dios Pérez, Young Jin Suh (2007)

Czechoslovak Mathematical Journal

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This paper consists of two parts. In the first, we find some geometric conditions derived from the local symmetry of the inverse image by the Hopf fibration of a real hypersurface $M$ in complex space form $M_{m} (4 ϵ)$ . In the second, we give a complete classification of real hypersurfaces in $M_{m} (4 ϵ)$ which satisfy the above geometric facts.

Isoparametric and Dupin hypersurfaces.

Cecil, Thomas E. (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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On real hypersurfaces of type $A$ in a complex space form. III.

Kim, Hyang Sook, Pyo, Yong-Soo (1998)

Balkan Journal of Geometry and its Applications (BJGA)

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Parallel hypersurfaces

Barbara Opozda, Udo Simon (2014)

Annales Polonici Mathematici

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We investigate parallel hypersurfaces in the context of relative hypersurface geometry, in particular including the cases of Euclidean and Blaschke hypersurfaces. We describe the geometric relations between parallel hypersurfaces in terms of deformation operators, and we apply the results to the parallel deformation of special classes of hypersurfaces, e.g. quadrics and Weingarten hypersurfaces.

Characterization of totally umbilic hypersurfaces in a space form by circles

Toshiaki Adachi, Sadahiro Maeda (2005)

Czechoslovak Mathematical Journal

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In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda.

Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting shape operator

Juan de Dios Pérez, Young Jin Suh, Changhwa Woo (2015)

Open Mathematics

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In this paper we prove a non-existence of real hypersurfaces in complex hyperbolic two-plane Grassmannians SU2.m/S(U2·Um), m≥3, whose structure tensors {ɸi}i=1,2,3 commute with the shape operator.